The Astrophysical Journal, 751:46 (15pp), 2012 May 20 doi:10.1088/0004-637X/751/1/46C© 2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

THE DYNAMICS AND METALLICITY DISTRIBUTION OF THE DISTANT DWARF GALAXY VV124∗

Evan N. Kirby1,3, Judith G. Cohen1, and Michele Bellazzini21 California Institute of Technology, 1200 East California Boulevard, MC 249-17, Pasadena, CA 91125, USA

2 INAF-Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, ItalyReceived 2011 December 14; accepted 2012 March 19; published 2012 May 3

ABSTRACT

VV124 (UGC 4879) is an isolated, dwarf irregular/dwarf spheroidal (dIrr/dSph) transition-type galaxy at a distanceof 1.36 Mpc. Previous low-resolution spectroscopy yielded inconsistent radial velocities for different componentsof the galaxy, and photometry hinted at the presence of a stellar disk. In order to quantify the stellar dynamics, weobserved individual red giants in VV124 with the Keck/Deep Extragalactic Imaging Multi-Object Spectrograph(DEIMOS). We validated members based on their positions in the color–magnitude diagram, radial velocities, andspectral features. Our sample contains 67 members. The average radial velocity is 〈vr〉 = −29.1 ± 1.3 km s−1

in agreement with the previous radio measurements of H i gas. The velocity distribution is Gaussian, indicatingthat VV124 is supported primarily by velocity dispersion inside a radius of 1.5 kpc. Outside that radius, ourmeasurements provide only an upper limit of 8.6 km s−1 on any rotation in the photometric disk-like feature. Thevelocity dispersion is σv = 9.4 ± 1.0 km s−1, from which we inferred a mass of M1/2 = (2.1 ± 0.2) × 107 M�and a mass-to-light ratio of (M/LV )1/2 = 5.2 ± 1.1 M�/L�, both measured within the half-light radius. Thus,VV124 contains dark matter. We also measured the metallicity distribution from neutral iron lines. The averagemetallicity, 〈[Fe/H]〉 = −1.14 ± 0.06, is consistent with the mass–metallicity relation defined by dSph galaxies.The dynamics and metallicity distribution of VV124 appear similar to dSphs of similar stellar mass.

Key words: galaxies: abundances – galaxies: dwarf – galaxies: individual (VV124) – galaxies: kinematics anddynamics – Local Group

Online-only material: color figures, machine-readable table

1. INTRODUCTION

The dwarf galaxy VV124 is one of the “newest” members ofthe local universe. The discovery of VV124 was first publishedin the Vorontsov-Velyaminov (1959) Atlas and Catalog ofInteracting Galaxies, though the galaxy does not have aninteracting neighbor. The CfA galaxy redshift survey (Huchraet al. 1983) reported its redshift as cz = 600 ± 100 km s−1.In the Hubble flow, this redshift corresponds to a distance of∼10 Mpc. At that distance, VV124 would have belonged to agroup of three galaxies (Turner & Gott 1976; Geller & Huchra1983). However, Kopylov et al. (2008) noticed resolved starsin Sloan Digital Sky Survey images (Adelman-McCarthy et al.2007). Kopylov et al. imaged VV124 to a depth of V = 25.6, andthey confirmed that it is in fact much nearer than 10 Mpc. Theymeasured a distance of 1.1 ± 0.1 Mpc based on the tip of the redgiant branch (TRGB). This new distance placed the galaxy onthe periphery of the Local Group. Despite its proximity to thegroup, VV124 is extremely isolated. Its nearest neighbor, LeoA, is another isolated dwarf galaxy 700 kpc away (Jacobs et al.2011).

The revision to VV124’s distance drastically affected its in-ferred star formation history. From low-resolution spectroscopy,James et al. (2004) measured its Hα star formation rate as(5.0 ± 2.4)×10−3 M� yr−1, but that rate was based on a distanceof 10.5 Mpc. Corrected to the true distance of 1.36 Mpc (Jacobset al. 2011), the rate dropped to 8.4×10−5 M� yr−1 (a point also

∗ The data presented herein were obtained at the W. M. Keck Observatory,which is operated as a scientific partnership among the California Institute ofTechnology, the University of California, and the National Aeronautics andSpace Administration. The Observatory was made possible by the generousfinancial support of the W. M. Keck Foundation.3 Hubble Fellow.

noted by Bellazzini et al. 2011a, hereafter B11a). The new dis-tance also inspired deep photometry in addition to that obtainedby Kopylov et al. (2008). B11a obtained wide-field g, r photom-etry of VV124 at the Large Binocular Telescope (LBT) to studythe structure of the galaxy in detail. Jacobs et al. (2011) obtainedeven deeper V and I photometry over a smaller field with theHubble Space Telescope (HST) Advanced Camera for Surveys.They determined that 93% of the stars are older than 10 Gyr.The rest are younger than 1 Gyr. Bellazzini et al. (2011b) usedthe same HST images as Jacobs et al. to show that the oldest,most metal-poor population is significantly more extended thanthe younger stars. The galaxy-averaged star formation rates thatJacobs et al. derived were (3.0 ± 0.2) × 10−4 M� yr−1 over thelast 0.5 Gyr and (8.0 ± 0.5) × 10−4 M� yr−1 over the last 1 Gyr.Together, the HST photometry and Hα spectroscopy indicatedthat VV124 is a typically old dwarf galaxy that experienced asmall burst of star formation ∼1 Gyr ago.

Tikhonov et al. (2010) expanded Kopylov et al.’s (2008)study. They classified VV124 as transition-type galaxy, caughtbetween being a dwarf irregular (dIrr) and a dwarf spheroidal(dSph) galaxy. They noticed that the young, blue stars lie in athin, disk-like structure, whereas the older, red giants occupy athicker configuration. However, the small number of very youngstars was inconsistent with an irregular-only classification.Therefore, they concluded that VV124 is a rare dIrr/dSphgalaxy. Grebel et al. (2003) listed only five other such membersof the Local Group: Antlia, Aquarius, Phoenix, Pisces, andKKR 25. This class of galaxies is especially interesting becausetheir existence supports the theory that dSphs are dIrrs that losttheir gas through ram pressure stripping and tidal interactionswith other galaxies (Mayer et al. 2001a, 2001b, 2006, 2007).There is strong observational support for the removal of gasfrom dwarf galaxies in dense environments (e.g., Geha et al.

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

2006; Grcevich & Putman 2009), and the similarity of thestar formation histories except in the past Gyr of dIrrs, dSphs,and dIrr/dSphs further supports the transformation of dIrrs intodSphs (Weisz et al. 2011). Although there are counterexamples,such as the comparatively young Leo A dIrr (Cole et al. 2007),the star formation history of VV124 less recent than 1 Gyrappears much like other dIrrs and dSphs. Except for the recentburst, Jacobs et al. (2011) reported that almost all of its stars areancient, like nearly all dSphs.

The dynamics of VV124 have been unclear. Despite thecorrected redshift, measurements of the galaxy’s radial velocityhave been inconsistent. Kopylov et al. (2008) and Tikhonov et al.(2010) obtained low-resolution spectroscopy of individual stars,resolved H ii regions, diffuse stellar light, and diffuse emission.The velocities varied widely, but they seemed to cluster aroundvr = −70 km s−1. B11a measured the H i velocity structurewith the Westerbork Synthesis Radio Telescope. They measureda heliocentric radial velocity of vr = −25 ± 4 km s−1 witha dispersion of ∼11 km s−1 and a full range of about −45 to0 km s−1. B11a also measured the velocities of a blue supergiantand a young star cluster, but the cluster velocity was inconsistentwith (more negative than) the H i velocity by 2.7σ . So far,the discrepancy between the velocities of the neutral gas andyounger populations has not been resolved.

B11a also observed what appears to be a stellar disk. VV124is elongated (ε = 0.44 ± 0.04, P.A. = 84◦ ± 11◦), but its shapecannot be described by a single ellipsoid. There is an even moreelongated component whose major axis is aligned with the mainspheroid. The second component, which B11a called “wings,”resembles a stellar disk, which should rotate coherently, unlikethe spheroid. As an alternative, B11a also proposed that thewings might be tidal tails instead of a disk. However, VV124’sextreme isolation makes strong tidal interaction unlikely.

In order to provide closure to the discrepancies in velocitymeasurements and to test for rotation, we observed red giantsin VV124 with the Deep Extragalactic Imaging Multi-ObjectSpectrograph (DEIMOS; Faber et al. 2003) on the Keck IItelescope. The median velocity uncertainty of the individualstellar measurements is 4.1 km s−1, which is small enoughto test for the presence of dark matter. The spectra are also ofsufficient quality to measure metallicities from neutral iron lines.The median uncertainty in metallicity is 0.21 dex. This articlepresents the results of our dynamics and metallicity studies.

2. OBSERVATIONS AND REDUCTIONS

2.1. Target Selection

Targets were selected from B11a’s photometric catalog.DEIMOS slitlets cannot overlap in the dispersion direction, andthe VV124 field is dense enough that we needed to prioritizethe targets for placement on the DEIMOS slitmasks. Thetargets were prioritized by magnitude and physical location withrespect to the center of VV124. Brighter targets were preferredfor higher signal-to-noise ratios (S/Ns). We defined X as thedistance along the major axis and Y as distance along the minoraxis. This is the same nomenclature introduced by B11a.

We used the dsimulator4 program to select targets forplacement on DEIMOS slitmasks. The program maximizes thenumber of high-priority targets within user-defined constraints.We required slitlets to be at least 4′′ long and separated by 0.′′35for adequate sky subtraction. Slit widths were 0.′′7, a choice that

4 http://www.ucolick.org/∼phillips/deimos_ref/masks.html

0.0 0.5 1.0 1.5 2.0g − r

24

23

22

21

r

25

24

23

22

V

Priority12345

Priority12345

Figure 1. CMD from LBT photometry (B11a). Colored points identify starsselected for DEIMOS spectroscopy. The color signifies the priority of the starfor spectroscopic selection (Section 2.1). Filled points are spectroscopicallyconfirmed member stars, and hollow points are non-members. The right axisgives the approximate Cousins V magnitude.

(A color version of this figure is available in the online journal.)

balanced observing efficiency with spectral resolution, whichcorresponds to precision in the radial velocity and metallicitymeasurements.

We prioritized targets for spectroscopy in the following order.

1. Brighter red giant branch (RGB) candidates near the majoraxis (V � 23.7 and |Y | � 2′).

2. Fainter RGB candidates near the major axis (V > 23.7 and|Y | � 2′).

3. Bright, blue non-RGB stars near the major axis (V � 23.7,g − r < 1.1, and |Y | � 2′).

4. RGB candidates away from the major axis (|Y | > 2′).5. Any other non-RGB candidates.

RGB candidates are defined as r > 22 and 0.7 < g − r < 1.4.One pair of slitmasks comprised our observations. The

slitmasks, subtending roughly 16′ × 4′, were roughly centeredon the galaxy at position angles (P. As.) of 86◦ and −94◦(i.e., rotated 180◦). The target lists for the two slitmasks werealmost identical. This ensured that we had two independentmeasurements of the radial velocities for almost all of the stars.The target list included 131 unique targets, of which 106 wereincluded on both slitmasks.

Figure 1 shows the color–magnitude diagram (CMD) forVV124. Spectroscopic targets are identified by colored points.Filled points indicate spectroscopically confirmed member stars(see Section 4). The colors correspond to the priorities in thelist above. Figure 2 shows the coordinates of the stars with thesame color coding.

2.2. Observations

We observed the two slitmasks, called vv124a and vv124b, on2011 January 30 (UT). Table 1 lists the exposure times, seeing,number of targets, and number of VV124 members for eachslitmask. The following night was also allocated to this project,but high humidity and fog on that night prevented any observingof VV124.

We used the 1200 lines mm−1 grating centered at 7800 Å.This grating, combined with the slit widths of 0.′′7, yielded

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

5 0 -5Δα (arcmin)

-2

0

2

4

Δδ (

arcm

in)

-3 -2 -1 0 1 2 3

Δ x (kpc)

-1

0

1

Δy

(kpc

)

N

E

Figure 2. DEIMOS slitmask footprints overlaid on the LBT astrometric catalog (B11a). The colors and types of points have the same meanings as in Figure 1. Theaxis labels give the displacement from the center of VV124 (α0 = 9h16m03s, δ0 = +52◦50′31′′). The top and right axes give this displacement in kpc for an assumeddistance of 1.36 Mpc (Jacobs et al. 2011). The positions and shapes of the two DEIMOS slitmasks are outlined.

(A color version of this figure is available in the online journal.)

Table 1DEIMOS Observations

Mask Seeing Targets Members Total Exposure Time Individual Exposure Times(′′) (s) (s)

vv124a 0.57–0.87 121 61 13200 6 × 1800, 2 × 1200vv124b 0.55–0.65 120 64 13600 6 × 1800, 1600, 1200

a line spread profile with an FWHM of 1.2 Å. The resolvingpower is about R ∼ 7000 near the Ca ii triplet (CaT) at 8500 Å.We obtained a 1 s exposure of internal Ne, Ar, Kr, and Xe arclamps for wavelength calibration and three 12 s exposures ofan internal quartz lamp for flat fielding. Although DEIMOSis mounted on the Nasmyth platform of Keck II, it rotates totrack the sky. An active flexure compensation system maintainsstability to within 0.2 pixels, corresponding to 3 μm on the focalplane, which is equivalent to 0.′′02 in the spatial direction and to0.07 Å in the dispersion direction.

Individual exposure times for the VV124 slitmasks rangedfrom 20 to 30 minutes. Most of the exposures were 30 minutes.We checked the alignment of the slitmask about once per hour byplacing the grating in zeroth order. In this direct imaging mode,bright alignment stars aligned with 4′′ boxes in the slitmask. Wemeasured the seeing by fitting Gaussian profiles to the point-spread functions of the alignment stars. Seeing remained lowand stable for the entire night (see Table 1).

2.3. Reductions

We reduced the raw images into one-dimensional spectrawith the spec2d5 software developed by the Deep ExtragalacticEvolutionary Probe 2 team (Davis et al. 2003). The softwareexcised the footprint of each spectrally dispersed slitlet fromeach exposure of the flat field, arc lamps, and science targets.Because the DEIMOS focal plane is curved, the programrectified the slitlet images by tracing and straightening boththe edges of the flat field and the roughly orthogonal arc lines.Then, the program generated a flat-field image from the threeexposures of the quartz lamp. This flat field was used to removethe slit response function, dust, and cosmetic imperfections inthe science images. The spec2d software also fitted a fifth-orderLegendre polynomial in wavelength to the pixel positions of arc

5 http://deep.berkeley.edu/spec2d/

lines. For each exposure of each slitlet, spec2d computed thesky emission as a function of wavelength and subtracted it fromthe two-dimensional spectrum. All of the science exposures foreach slitmask were averaged with inverse variance weightingand cosmic-ray rejection. Finally, the object spectrum wasextracted with optimal weighting (Horne 1986). The final resultwas a clean, one-dimensional spectrum, wavelength-calibratedto a precision of 0.01 Å. The spectrum was not flux-calibrated,and it did not need to be for our purposes.

Some spectra suffered from artifacts or such low S/N thatmeasurement of the radial velocity was not possible. There were13 such spectra. They are included and identified in Table 2, butwe do not consider them further.

The spec2d software also computed the error spectrum fromPoisson statistics of the raw frame. The errors were adjustedappropriately during flat fielding, and the one-dimensional errorspectrum was extracted identically to the flux spectrum. Weused the error spectra for estimation of uncertainties in radialvelocities (Section 3) and metallicities (Section 6).

As mentioned in Section 2.1, the two slitmasks included 106duplicate targets. We measured the precision of our velocitymeasurements using the independently measured radial veloci-ties from the two slitmasks. However, for the final list of radialvelocities, we used a combined spectrum. We summed the twoone-dimensional spectra for each duplicate object with inversevariance weighting.

We removed telluric absorption using archived DEIMOSspectra of hot stars. We used the same hot star spectra andspectral division procedure as Kirby et al. (2008). However, ourscience exposures took place over an entire night. The vary-ing airmass and water vapor made it impossible to remove thetelluric absorption accurately. Regions of moderately strong tel-luric absorption were not considered for metallicity measure-ments.

The metallicity measurements discussed in Section 6 requirednormalization of the spectral continuum. We followed the

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

Table 2Target List

ID R.A. Decl. g r Masksa S/N vr EW(Na i 8190) [Fe/H] Member? Reasonb

(J2000) (J2000) (Å−1) (km s−1) (Å)

13585 09 15 09.6 +52 49 52.0 24.351 ± 0.030 23.295 ± 0.043 1 4.1 . . . . . . . . . N G16765 09 15 10.8 +52 48 34.1 25.600 ± 0.038 23.667 ± 0.046 1 2.9 . . . . . . . . . N Bad11688 09 15 11.8 +52 50 12.4 25.268 ± 0.029 23.365 ± 0.025 1 15.5 . . . . . . . . . N G16355 09 15 11.8 +52 48 50.4 24.183 ± 0.011 23.125 ± 0.016 1 3.5 . . . . . . . . . N Bad16895 09 15 13.4 +52 48 29.4 24.198 ± 0.021 23.337 ± 0.032 1 2.9 . . . . . . . . . N Bad3705 09 15 15.4 +52 51 59.3 24.651 ± 0.015 23.217 ± 0.018 1 25.6 +31.5 ± 2.7 3.21 ± 0.24 . . . N vr Na16598 09 15 16.9 +52 48 40.7 23.009 ± 0.006 21.553 ± 0.007 1 50.9 −68.1 ± 2.4 2.22 ± 0.06 . . . N vr Na bright16798 09 15 17.5 +52 48 32.7 22.361 ± 0.006 20.841 ± 0.007 1 68.8 −25.5 ± 2.3 2.45 ± 0.04 . . . N Na bright7035 09 15 17.9 +52 50 58.8 22.720 ± 0.010 22.720 ± 0.013 2 16.5 . . . . . . . . . N G7917 09 15 19.8 +52 50 49.5 24.287 ± 0.012 23.183 ± 0.017 2 13.0 −40.1 ± 4.8 . . . −1.02 ± 0.21 Y

Notes. Identifications, coordinates, and photometry from B11a.a Number of DEIMOS masks on which the object was observed.b Reasons for non-membership. vr : inappropriate radial velocity. Na: spectrum shows strong Na i λ8190 doublet. G: spectrum shows emission lines or redshifted CaH and K lines, indicating that the object is a galaxy. Bright: target is brighter than the TRGB. Bad: spectral quality was insufficient for radial velocity measurement.

(This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content.)

continuum normalization procedure described by Kirby et al.(2009, their Section 3.4). After normalization, we calculated theS/N of each spectrum. First, we computed the median absolutedeviation (m.a.d.) from the continuum of pixels in “continuumregions” (defined by Kirby et al. 2008) in the rest wavelengthranges 7400–7500 Å, 7750–8100 Å, and 8400–8900 Å. Theseselections excluded most telluric absorption and TiO bands.Then, we removed all pixels that exceeded five times the m.a.d.and re-calculated the m.a.d. with this slightly trimmed set ofpixels. The result was the S/N per pixel. To convert to S/N per Å,we multiplied by

√1/0.33, where 0.33 is the pixel scale in Å

per pixel. This measurement of S/N is sensitive to inaccuraciesin the continuum placement, which will artificially decrease theS/N. However, errors in continuum placement dominate theS/N calculation only at S/N � 60 Å−1, which is much higherthan any member star in our sample.

3. RADIAL VELOCITY MEASUREMENTS

We measured radial velocities and their uncertainties follow-ing the procedure of Simon & Geha (2007). First, we measuredthe radial velocity of the star by cross-correlating the observedspectrum with a library of template stars and galaxies observedwith DEIMOS. The template spectra were the same as thoseused by Simon & Geha. They were observed with a nearly iden-tical configuration of DEIMOS and therefore have the same res-olution as our science spectra. The strong atmospheric A and Bbands (7588–7700 Å and 6862–6950 Å) were excluded from thecross-correlation. Three weaker telluric bands (7167–7315 Å,8210–8325 Å, and 8900–9200 Å) were given weights of 10%of other pixels in the cross-correlation. We adopted the veloc-ity corresponding to the cross-correlation peak of the templatewith the lowest χ2 when compared to the observed spectrum. Wecall this velocity vobj. Figure 3 shows typical spectra of VV124member stars along with the best-fitting template spectra.

Next, we computed a correction for mis-centering of the starin the slitlet (Sohn et al. 2007). For this step, we used theobserved spectrum before correction for telluric absorption. Wecross-correlated this spectrum with the spectrum of HR 1641,a hot, rapidly rotating star. Only regions subject to significanttelluric absorption (the same regions used by Simon & Geha2007) were considered in the cross-correlation. We call thevelocity obtained from this cross-correlation vtell. The radial

velocity of the star is vr = vobj − vtell − vhelio, where vheliois the heliocentric velocity correction appropriate for KeckObservatory on the observation date.

We estimated uncertainties in vr by Monte Carlo resamplingof the spectra. For each of 1000 realizations, we added Gaussianrandom noise to the spectrum. The dispersion of the Gaussianprobability distribution at each pixel was equal to the estimatedPoisson error of that pixel. Then, we recomputed vobj and vtell foreach realization. For computational efficiency, we consideredonly the template spectrum that best matched the originalspectrum. The standard deviation of the 1000 measurementsof vr is σMC.

From duplicate vr measurements of the same stars, Simon& Geha realized that σMC was an incomplete estimate of theradial velocity uncertainty. In order to explain the dispersionamong the repeat measurements, they added a systematic errorterm, σsys, in quadrature with σMC. The systematic term waschosen such that the radial velocity differences divided by theirtotal uncertainties were distributed normally with unit standarddeviation:

√√√√ 1

N

N∑i=1

(vr,1 − vr,2)2

σ 2MC,1 + σ 2

MC,2 + 2σ 2sys

= 1. (1)

Because we observed 106 duplicate objects on both DEIMOSslitmasks, we also calculated a systematic error term. Weexcluded galaxies, obvious foreground dwarfs with Na i 8190absorption, and other objects failing any membership criterionother than radial velocity (see Section 4). From the 57 remainingstars, we computed σsys = 2.21 km s−1—which is the samevalue that Simon & Geha derived—by solving Equation (1).Figure 4 shows the distribution of differences in repeat vr

measurements divided by their estimated uncertainties. Thewidth of the distribution matches a unit Gaussian because σsyswas tuned to force such a match.

Figure 5 shows how velocity errors and uncertainties trendwith S/N. The vr differences between repeat measurements(top panel) are based on exposures from one slitmask only.Therefore, their S/Ns are about 1/

√2 of the S/N of the stacked

spectra used for remainder of our analysis. The estimateduncertainties (bottom panel) decrease with increasing S/N, as

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

0.2

0.4

0.6

0.8

1.0

texp = 447 min.SNR = 23.8 Å−1r = 22.6913105

texp = 447 min.SNR = 23.8 Å−1r = 22.6913105

0.2

0.4

0.6

0.8

1.0

norm

aliz

ed f

lux

texp = 447 min.SNR = 10.4 Å−1r = 23.4314111

texp = 447 min.SNR = 10.4 Å−1r = 23.4314111

8450 8500 8550 8600 8650 8700rest wavelength (Å)

0.2

0.4

0.6

0.8

1.0

texp = 220 min.SNR = 7.1 Å−1r = 23.1211816

texp = 220 min.SNR = 7.1 Å−1r = 23.1211816

Figure 3. DEIMOS spectra of three red giant members of VV124. Only a small portion of the spectrum around the CaT is shown. For display, the spectra have beennormalized to the continuum and smoothed with a Gaussian kernel (σ = 0.7 Å). The radial velocity template spectrum, provided by Simon & Geha (2007), is shownin red in all three panels. The top and bottom panels show the spectra with the highest and lowest S/Ns in our sample. The middle panel shows the faintest memberstar in our sample.

(A color version of this figure is available in the online journal.)

expected. Only the random error term, σMC, decreases withS/N. The systematic error term, σsys, is constant.

4. MEMBERSHIP

We used several criteria for determining membership. First,we eliminated stars based on their positions in the CMD. Then,we eliminated stars with spectral features not found in red giants.Finally, we eliminated stars based on their radial velocities.

4.1. Color–Magnitude Diagram

B11a identified the extinction-corrected magnitude of theTRGB as r0 = 22.61 ± 0.06. In selecting spectroscopictargets, we prioritized stars with r > 22, which conservativelyallowed for large error in the TRGB magnitude. It also allowedsome asymptotic giant branch (AGB) stars. In order to fill theslitmasks, we also included some targets with r � 22.

Stars brighter than the TRGB are not likely members. Wecarefully examined all stars with r0 < 22.49 (2σ brighter thanthe TRGB). After excluding stars failing to meet the membershipcriteria in the following sections, four stars remained. Star8116 showed broad CaT lines. The width and shape suggested

pressure broadening typical of dwarf stars. Therefore, we ruled8116 as a non-member. The spectrum of star 8445 looked in allrespects like a red giant. Although the star is slightly brighterand bluer than the TRGB, we kept 8445 in the member list underthe premise that it is an AGB star. The spectrum of star 11163showed very strong cyanogen bands. If this carbon star is anAGB member of VV124, it could be significantly brighter andredder than the TRGB. In fact, that is its location in the CMD.For this reason, we kept 11163 in the membership list. Finally,star 13649 is solidly in the “wall” of foreground dwarfs in theCMD, and its Na i 8190 equivalent width (EW) is very closeto the cutoff for membership (see the next section). We ruled13649 a foreground dwarf for the combination of its position inthe CMD and moderately strong Na i 8190 doublet.

4.2. Spectral Features

Inspection of the DEIMOS spectra revealed that many of ourtargets were background galaxies or foreground dwarf stars.First, we excluded all objects with emission lines or broad,redshifted Ca H and Ca K in absorption. These 20 objects arebackground galaxies.

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

−3 −2 −1 0 1 2 3(vr,1 − vr,2) / (σMC,1

2 + σMC,22 + 2σsys

2)1/2

0

2

4

6

8

10

12

14

N

Figure 4. Radial velocity measurement differences of the same stars observedon two different slitmasks. The differences are divided by the quadrature sum ofthe measurement uncertainties, which include noise and systematic error terms.The solid curve is a Gaussian with unit standard deviation. The systematic errorterm, σsys, was adjusted to ensure that the standard deviation is unity.

0

5

10

15

20

|v r,1 −

vr,

2| (k

m s

−1)

Repeat measurements(partial exposures)

5 10 15 20 25SNR (Å−1)

0

2

4

6

8

10

(σM

C2 +

σsy

s2 )1/2 (

km s

−1) Member stars

(full exposures)

Figure 5. Top: absolute radial velocity differences of repeat measurements ofthe same stars on two different slitmasks vs. S/N. These measurements werenecessarily based on spectra with about half the exposure time of the final,stacked spectra. Bottom: estimated error on vr as a function of S/N for allmember stars. The total error is the quadrature sum of the random (MonteCarlo) and systematic error terms.

Second, we excluded stars with very strong, broad Na i 8190doublets. The strengths of these lines are especially sensitive tosurface gravity. That sensitivity makes them excellent discrim-inators between giants and foreground dwarf stars (Spinrad &Taylor 1971; Cohen 1978; Schiavon et al. 1997; Gilbert et al.2006). We measured the EWs of each of the two lines in the

0 1 2 3 4 5log g

0.0

0.5

1.0

1.5

2.0

2.5

EW

(Na

8190

) (Å

)

[Na/H] =

+0.0

−0.5−1.0−1.5−2.0

Figure 6. Summed EW of the Na i 8190 doublet as a function of surface gravityand [Na/H]. The summed EW exceeds 1 Å only for dwarf stars (log g > 4.5).

doublet by fitting two independent Gaussians. We com-puted Monte Carlo uncertainties by resampling the spectrum100 times. For each pixel in each resample, we added noisefrom a Gaussian random distribution with a standard deviationequal to the estimated Poisson noise of that pixel. We fittedGaussians to each resample, and we adopted the standard devi-ation among their EWs as the error on the EW. Table 2 gives thesummed EWs and their uncertainties for stars where the doubletwas measurable above the noise.

We computed a threshold value for the summed EW of thedoublet by looking up EWs in a grid of non-local thermody-namic equilibrium (NLTE) Na abundances (Lind et al. 2011).We sampled EWs from log g = 0.5 to 4.7 and [Na/H] = 0.0to −2.0. We found the appropriate effective temperature foreach combination of surface gravity and abundance (assum-ing [Na/Fe] = 0) from a 10 Gyr Yonsei–Yale isochrone(Demarque et al. 2004). Interpolations in the NLTE grid yieldedFigure 6. Some points are missing from the figure because theyare also missing from the NLTE grid. Regardless, it is clearthat the doublet increases sharply in EW for dwarf stars withlog g > 4. The summed EW of the doublet exceeds 1 Å forstars with [Na/H] � 0 only at surface gravities log g > 4.5. Weidentified 17 stars with a summed Na i 8190 EW greater than1 Å. These 17 stars are foreground dwarfs.

Counting star 8116, excluded for its broad calcium lines andfor being brighter than the TRGB, we eliminated 38 objectsbased on spectral features. Another three stars showed strongCN bands. One of these, 11163, is discussed in Section 4.1. Theother two stars, 9378 and 13043, pass all membership criteria,and we retained them as members.

4.3. Radial Velocities

The median radial velocity uncertainty in our sample of mem-ber stars is 4.1 km s−1, on the order of the velocity dispersionof a small dSph. Therefore, it is important to consider velocityerrors carefully when computing the velocity dispersion. Walker

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

Table 3Properties of VV124

Property Symbol Value

Photometry

Distancea D 1.36 ± 0.03 MpcLuminosityb LV 8.2+1.6

−1.4 × 106 L�Stellar massc M∗ 9.4+3.8

−2.9 × 106 M�Gas massb Mgas 8.7 × 105 M�Half-light radiusb Re 41.′′3 = 260 pc

Dynamics

Mean radial velocity 〈vr 〉 −29.1 ± 1.3 km s−1

Line-of-sight velocity dispersion σv 9.4 ± 1.0 km s−1

Mass within half-light radiusd M1/2 (2.12 ± 0.22) × 107 M�Mass-to-light ratio within half-light radiusd (M/LV )1/2 5.2 ± 1.1 M�/L�Dynamical-to-stellar mass ratio within half-light radiusc,d (Mdyn/M∗)1/2 4.5 ± 1.9Total masse Mtot (1.95 ± 0.40) × 107 M�Total mass-to-light ratioe (M/LV )tot 4.8 ± 1.3 M�/L�

Metallicity

Mean metallicityf 〈[Fe/H]〉 −1.14 ± 0.06Standard deviation σ ([Fe/H]) 0.49Median metallicity med([Fe/H]) −1.08Median absolute deviation mad([Fe/H]) 0.26Interquartile range IQR([Fe/H]) 0.54Skewness Skew([Fe/H]) −0.64 ± 0.31Kurtosis Kurt([Fe/H]) −0.05 ± 0.60Yield (simple model) p (Simple) 0.117+0.016

−0.016 Z�Yield (pre-enriched model) p (Pre-Enriched) 0.117+0.020

−0.017 Z�Initial metallicity (pre-enriched model) [Fe/H]0 <−2.66Yield (extra gas model) p (Extra Gas) 0.109+0.014

−0.012 Z�Extra gas parameter (extra gas model) M 4.76+9.79

−2.30

Notes.a Jacobs et al. (2011).b B11a.c Although B11a assumed M∗/LV = 2, we assumed that M∗/LV = 1.10, a value more typical of transition-type dwarfs(Woo et al. 2008). We used this stellar mass-to-light ratio to calculate these quantities. The value could range from 0.8 to1.5, and we took these limits into account in the estimation of the uncertainties.d Using the formula M1/2 = 4G−1Reσ

2v (Wolf et al. 2010).

e Using the formula Mtot = 167μrcσ2v (Illingworth 1976), which may not be appropriate for VV124. This formula often

gives smaller Mtot than the formula for M1/2.f Although Kirby et al. (2011a) calculated 〈[Fe/H]〉 with inverse variance weighting, we present the unweighted mean.The low S/Ns of many of our spectra cause the error on [Fe/H] to increase strongly with decreasing metallicity. Therefore,the weighted mean would be biased toward high [Fe/H].

et al. (2006) devised a formalism to take these errors into ac-count. The procedure involved maximizing the likelihood thatthe average radial velocity, 〈vr 〉, and the intrinsic velocity disper-sion, σv , accurately describe the observed velocity distributionof candidate member stars in the presence of observational error.The process was iterative. We chose 〈vr〉 = −30 km s−1 andσv = 9 km s−1 as rough guesses for the first iteration. In eachsubsequent iteration, only stars within 2.58σv (99% of a normaldistribution) of 〈vr〉 were considered. In fact, just one iterationwas required to converge on the final member sample and thefinal values of 〈vr〉 and σv . The uncertainties on 〈vr〉 and σv

were determined from the likelihood covariance matrix. Table 3gives the fiducial values for 〈vr〉 and σv and their uncertainties.

We used 〈vr〉 and σv to determine the final membership cut.If a normal distribution is a good description of the velocitydistribution, then the velocity range 〈vr〉 ± 2.58σv includes99% of the members. This cut excluded 6 stars and retained67 members. Some galaxy dynamics studies suggest that a cutof 3σ is a better choice. Adopting a 3σ cut for VV124 wouldnot have affected the membership of any star.

Table 2 lists all of the spectroscopic targets. The table givesastrometric and photometric data, as well as quantities derivedfrom the spectra. The last two columns of the table indicatewhether the object is a member star and the reasons that starswere considered non-members.

Figure 7 presents the velocity distribution of VV124. Thevelocities are distributed normally. The skewness, a measure ofasymmetry, of the vr distribution is 0.14 ± 0.29. The kurtosis,a measure of the deviation from Gaussianity, is −0.26 ± 0.58.Both parameters are consistent with zero, indicating confor-mance to a normal distribution. The vertical, dashed lines show〈vr〉±2.58σv , and the solid curve shows a perfect normal distri-bution (not a fit) for those parameters, normalized to the numberof member stars.

5. DYNAMICS

5.1. Mean Radial Velocity and Velocity Dispersion

The mean radial velocity, 〈vr〉 = −29.1 ± 1.3 km s−1, agreeswith the radial velocity of the H i gas, 〈vr〉 = −25 ± 4 km s−1

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

−60 −40 −20 0 20vr (km s−1)

0

2

4

6

8

10

12

N

⟨vr⟩⟨vr⟩ = −29.1 ± 1.3 km s−1

σv σv = 9.4 ± 1.0 km s−1

Figure 7. Heliocentric radial velocity distribution. The solid curve is aGaussian distribution corresponding to the measured mean velocity and velocitydispersion. The dashed lines enclose 99% (±2.58σ ) of the member stars. Thefigure label gives the average heliocentric velocity and the velocity dispersioncorrected for measurement uncertainty (see Section 5). Only stars passing allmembership cuts except velocity are shown.

(B11a). The agreement is especially reassuring because previousoptical measurements of radial velocities showed significantlymore negative vr . Kopylov et al. (2008) and Tikhonov et al.(2010) observed two blue supergiants: bl1 with vr = −90 ±15 km s−1 and bl2 with vr = −82 ± 15 km s−1. They alsoestimated the average radial velocity of unresolved stellar lightto be 〈vr〉 = −70±15 km s−1. Radial velocities of resolved anddiffuse H ii gas, measured from the [O iii] 5007 emission line,ranged from −36 to −71 km s−1. B11a revised the velocityof the supergiant bl2 to vr = −44 ± 18 km s−1. They alsoobserved a star cluster, C1, with vr = −86 ± 20 km s−1

and diffuse Hα emission with 〈vr〉 = −6 ± 30 km s−1. Theindividual sources bl1, C1, and one of the H ii regions haveradial velocities more than 1σ inconsistent with our velocitycuts for membership. The stellar integrated light measurementof 〈vr〉 by Kopylov et al. and Tikhonov et al. is 2.7σ discrepantfrom our measurement. In every case, the discrepancies are suchthat the other measurements are more negative than ours. Weare confident that our measurement of 〈vr〉 is accurate becauseit agrees with the H i measurement. Moreover, our estimate isbased on higher resolution spectra and a much larger samplethan Kopylov et al. (2008), Tikhonov et al. (2010), and B11a.

There are two possible causes of the discrepancy. First, therecould have been some systematic error in the measurementsof vr from the low-resolution spectra of Kopylov et al. andTikhonov et al. The upward revision of vr for bl2 by B11a maysupport this conclusion. On the other hand, B11a also measureda very negative vr for the star cluster C1. We also note that weexcluded three stars with −75 km s−1 < vr < −55 km s−1 asnon-members because their velocities are too negative. Thesevelocities are similar to those of bl1 and C1. It may alsobe relevant that the H i gas southeast of the center of thegalaxy has more negative vr than the gas in the central regions(B11a). Thus, VV124 may have a non-equilibrium dynamical

component consisting of a young stars and star-forming regions.This component would have more negative vr than the old redgiants and neutral gas. The data available do not point to adefinitive conclusion. Higher resolution observations of bl1, C1,other young stars, and star-forming regions will better defineVV124’s velocity structure.

Unresolved binaries could inflate the velocity dispersion.Minor et al. (2010) concluded that this inflation is unlikely tobe more than 30% in galaxies with 4 km s−1 < σv < 10 km s−1.In a separate study, McConnachie & Cote (2010) arrived ata similar conclusion, but cautioned that even a modest binaryfraction could cause an ultra-faint dSph-sized stellar populationfree of dark matter to appear to have the velocity dispersionof a dark matter-dominated system. In a confirmation of thecontribution of unresolved binaries to mass estimates of dSphs,Koposov et al. (2011) revised the velocity dispersion of theBootes I dSph from >6 km s−1 (Munoz et al. 2006; Martin et al.2007) to two components: one population at 2.4 km s−1 anda smaller population at ∼9 km s−1. Most of this revision wasdue to a more precise estimation of velocity uncertainties, butremoving binaries did contribute to the reduction in σv .

We did not obtain multi-epoch spectroscopy for VV124.Therefore, we were unable to remove the contribution ofunresolved binaries. We suggest that the binary contributionto σv for VV124 is not nearly as large as for Bootes I orother ultra-faint dSphs. The warnings about the inflation ofvelocity dispersion by Minor et al. (2010), McConnachie &Cote (2010), and Koposov et al. (2011) specifically concernedthe ultra-faint dSphs with very low luminosities (<105 L�).VV124 does not fall into this class. Olszewski et al. (1996)showed that unresolved binaries inflate σv for the Ursa Minorand Draco dSphs by much less than 1 km s−1. Because thevelocity dispersion of VV124 is closer to the dispersions ofUrsa Minor and Draco than to ultra-faint dSphs, binarity likelydoes not dominate our measurement uncertainty.

5.2. Rotation

While B11a concluded that the H i gas in VV124 does notshow any signature of rotation, the interpretation of the stellarwings as an edge-on disk of stars prompted us to search forstellar rotation. If the structure is a disk, it is nearly edge-on,and rotation in principle should be evident in measurements ofstellar radial velocities.

VV124 also contains H i gas that has a velocity gradient of5–10 km s−1 across the face of the galaxy and a full velocityrange of ∼45 km s−1. However, the gradient is not alignedwith the disk-like structure. B11a suggested that the gradientarises not from rotation, but asymmetric stellar winds actingpreferentially on the southeast quadrant of the galaxy.

Based on B11a’s Figure 11 and our Figure 8, we definethe “wings” of VV124 as |X| � 4′ (1.6 kpc), where X isdistance along the major axis. Our sample includes eight suchmember stars. Therefore, we have spectroscopically confirmedthe existence of the photometrically feeble disk-like structurediscovered by B11a.

However, these stars show no evidence of rotation within thelimitations of our measurements. Figure 8 shows stellar radialvelocities versus distance from the minor axis. We quantifiedthe amount of rotation as ΔvEW, the difference between theaverage vr in the eastern and western wings. Our sample containssix members in the eastern wing and two members in thewestern wing. The velocity measurements of these stars yieldedΔvEW = 3.5 km s−1.

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

−60

−40

−20

0

20

v r (

km s

−1 )

RV memberRV non−memberforeground dwarf

(a)

−3 −2 −1 0 1 2 3distance along major axis (kpc)

−1

0

1

dist

ance

alo

ng m

inor

axi

s (k

pc)

(b)

N

E

Figure 8. (a) Heliocentric radial velocity as a function of displacement from the minor axis (distance along the major axis). Filled points are spectroscopic members,and hollow diamonds and crosses are non-members. The horizontal dashed line indicates 〈vr 〉. Only stars passing all membership cuts except velocity are shown. (b)Spatial locations of members and stellar non-members fainter than the TRGB. The gray lines are contours of equal surface density (B11a). From the inside to theoutside, the contours represent 3σ , 4σ , 5σ , 6σ , 7σ , 8σ , and 9σ differences from the central surface density.

In order to assess the precision of this measurement, weconstructed theoretical rotation curves for the outermost regionsof the galaxy. The curves were flat in the wings (r > 1.′5),and their magnitudes ranged from 0 to 20 km s−1, spaced at1 km s−1. We sampled the theoretical rotation curves with eightfake stars at the same distances along the major axis as the starsin our sample. Each fake star had a radial velocity perturbedfrom the rotation curve, and the amount of perturbation wassampled from a Gaussian random probability distribution witha standard deviation equal to the estimated uncertainty in vr

for the corresponding observed star. Under the assumptionthat any rotation would be diluted by incoherent velocitydispersion, we further perturbed each star’s velocity accordingto a Gaussian random distribution with a standard deviation ofσv , the previously measured line-of-sight velocity dispersion ofVV124. We computed ΔvEW for 1000 such Monte Carlo trialsfor each of the rotation curves. The standard deviation of theprobability distributions is an estimate of the uncertainty onthe observed value of ΔvEW = 3.5 km s−1. This uncertainty,8.6 km s−1, is insensitive to the magnitude of the rotation.

Our measurements are consistent with the absence of rotationbecause ΔvEW is consistent with zero. However, our data set islimited in its ability to detect rotation. Under the assumptionthat the velocity dispersion is constant with radius and that thisvelocity dispersion dilutes any rotation signal in the wings, theminimum rotation signal we could have detected is 8.6 km s−1.

The stars in the southeast of the galaxy do not have any morenegative vr than stars elsewhere. Therefore, our observations donot show a stellar counterpart to the asymmetric gas velocity.

Radial velocity measurements of bluer, younger stars mightshow such structure, but we have not performed suchobservations.

Our observations are not conclusive evidence against rotationor a stellar counterpart to the H i velocity structure. Furthermore,we may have misclassified some foreground stars as members.Such misclassifications may alter a rotation signal. We con-sidered the possibility that some true members may have beenmisclassified as foreground dwarfs based on the strength of theirNa i 8190 doublets (hollow diamonds in Figure 8), but the ra-dial velocities of those stars do not suggest rotation or velocitystructure any more than the spectroscopic members. We cannotrule out the possibility that a larger sample with more precisemeasurements of vr will detect velocity structure in the stars.

5.3. Mass

The mass of a spheroidal stellar system can be determinedfrom its line-of-sight velocity dispersion under the assumptionof a mass profile and velocity anisotropy. In the case of VV124,only stars and dark matter significantly affect σv . Gas is ir-relevant because the gas mass is just a small fraction of thestellar mass. Illingworth (1976) presented a formula to measurethe mass of globular clusters: Mtot = 167μrcσ

2v , where rc is

the King (1962) core radius and μ is a dimensionless number6

6 King (1966) and Illingworth (1976) called this parameter μ. Mateo (1998)and Simon & Geha (2007) called it β. Because β is typically used to representvelocity dispersion anisotropy, we have chosen to call the concentrationparameter μ.

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

that quantifies the mass concentration toward the system’s cen-ter. The core radius may be approximated in relation to Re, thehalf-light or effective radius, as follows: rc = 0.64Re. Mateo(1998) stated that μ = 8 is appropriate for low-concentrationKing profiles and therefore appropriate for most dwarf galax-ies. However, Illingworth’s (1976) formula assumes that massfollows light and that the velocity dispersion anisotropy β = 0.These two assumptions are appropriate for globular clusters butnot for dark matter-dominated galaxies. Wolf et al. (2010) pre-sented an alternative formula for the mass enclosed within thehalf-light radius: M1/2 = 4G−1Reσ

2v , where Re is the half-light

or effective radius. It is at this radius that β has the least influ-ence on the estimate of the enclosed mass. Inside and beyondRe, the enclosed mass becomes increasingly uncertain becauseβ is unknown when only line-of-sight velocities are known.Table 3 gives both Mtot from the Illingworth (1976) formulaand M1/2 from the Wolf et al. (2010) formula. As is typical fordwarf galaxies, M1/2 actually exceeds Mtot because the Illing-worth (1976) formula is inappropriate for dwarf galaxies. Notethat both of these formulae assume sphericity. The ellipticity ofVV124 (ε = 0.44, B11a) diminishes the accuracy of these massestimators for VV124.

The mass-to-light ratio within the half-light radius is(M/LV )1/2 = 5.2 ± 1.1 M�/L�. This value is too large fora mass dominated by stars alone. According to up-to-date stel-lar models (Percival et al. 2009), old (12 Gyr) and metal-poor([Fe/H] = −1, which is about the mean metallicity for VV124,as derived in Section 6) stellar populations without dark mat-ter exhibit M/LV � 2.5 M�/L�. Due to the contribution ofthe young population, the expected value for VV124 should belower. The ratio of the dynamical mass to the stellar mass withinthe half-light radius is (Mdyn/M∗)1/2 = 4.5 ± 1.9. (This valuedepends inversely on the assumed stellar mass-to-light ratio,M∗/LV . See footnote c in Table 3.) Therefore, we conclude thatthe mass of VV124 is dominated by dark matter.

B11a roughly estimated the mass-to-light ratio (M/LV ≈ 8)of VV124 from the H i velocity distribution. They assumed thatthe gravitational potential dominates the gas motion and that theH i distribution is spherical and isotropic. Their value is 1.5 timesour measurement of (M/LV )1/2. However, theirs was a roughestimate. The difference can be explained by their slightly largermeasurement of 11 km s−1 for the velocity dispersion, comparedto our measurement of 9.4 km s−1. Our measurement is moreaccurate because it is based on individual stars. The gas velocitydispersion could be sensitive to stellar feedback, especially inlight of Bellazzini et al.’s interpretation of stellar winds as thecause of the velocity gradient seen in the gas.

6. METALLICITY DISTRIBUTION

We measured iron abundances from Fe i lines in the DEIMOSspectra. Kirby et al. (2008, 2009, 2010) described the procedurethat we used for these measurements. We corrected the photom-etry for extinction with Schlegel et al.’s (1998) dust maps. Theaverage reddening was low (E(B − V ) ≈ 0.01). After we con-verted the extinction-corrected apparent magnitudes to absolutemagnitudes assuming (m − M)0 = 25.67 ± 0.04 (Jacobs et al.2011), we used 12 Gyr Padova isochrones (Girardi et al. 2002) toestimate the photometric effective temperature and surface grav-ity of each star. A large grid of synthetic spectra was searchedfor the best-fitting synthetic spectrum. In the search, temper-ature and [Fe/H] were varied. The temperature was assigneda probability distribution based on the uncertainty in the star’sposition in the CMD. This probability distribution was included

−3 −2 −1 0 1 2 3([Fe/H]1 − [Fe/H]2) / (σcovar,1

2 + σcovar,22 + 2σsys,[Fe/H]

2)1/2

0

2

4

6

8

10

N

Figure 9. Metallicity measurement differences of the same stars observed ontwo different slitmasks. The differences are divided by the quadrature sum ofthe measurement uncertainties, which include noise and systematic error terms.The solid curve is a Gaussian with unit standard deviation. The systematic errorterm, σsys,[Fe/H], was adjusted to ensure that the standard deviation is unity.Compare this figure to Figure 4.

in the χ2 minimization to find the best-fitting synthetic spectrum.In this way, the spectroscopic temperature was not allowed tostray far from the photometric temperature. (See Sections 4.5and 4.7 of Kirby et al. 2009 for more details.) The photometryand the spectroscopy shared roughly equal weight in determin-ing the final temperature. The photometry alone determined thesurface gravity.

In previous works based on this technique, the uncertainty in[Fe/H] (σ covar) was calculated in part from the covariance matrixin the Levenberg–Marquardt optimization. Various diagnosticsindicated that this random uncertainty term underestimated thefull error in the measurement. Therefore, a systematic errorterm, σsys,[Fe/H] = 0.113, was added in quadrature to the randomuncertainty. That term was calculated from spectra with a typicalexposure time of 1 hr. The exposure time for most spectra inthis work exceeds 7 hr. Therefore, errors in sky subtraction playa much larger role than in our previous works.

Because the spectral noise behavior assumes a differentcharacter than in the spectra from which the systematic errorterm was originally calculated, we re-evaluated the magnitudeof σsys,[Fe/H] using only the VV124 data set. In analogy toour calculation of radial velocity uncertainties, we examineddifferences in [Fe/H] between measurements of the same starson the two separate slitmasks. We determined σsys,[Fe/H] = 0.191from the following equation:

√√√√ 1

N

N∑i=1

([Fe/H]1 − [Fe/H]2)2

σ 2covar,1 + σ 2

covar,2 + 2σ 2sys,[Fe/H]

= 1. (2)

In other words, σsys,[Fe/H] = 0.191 is the value requiredto force 1σ agreement between the repeat measurements of[Fe/H]. Figure 9 shows that this agreement was achieved.

Figure 10 shows the relationship between the error or uncer-tainty on metallicity versus spectral S/N. The top panel shows

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

0.0

0.2

0.4

0.6

0.8

1.0|[F

e/H

] 1 −

[Fe/

H] 2

| Repeat measurements(partial exposures)

5 10 15 20 25SNR (Å−1)

0.0

0.1

0.2

0.3

0.4

(σco

var2 +

σsy

s,[F

e/H

]2 )1/2 Member stars

(full exposures)

Figure 10. Top: absolute metallicity differences of repeat measurements ofthe same stars on two different slitmasks vs. S/N. These measurements werenecessarily based on spectra with about half the exposure time of the final,stacked spectra. Bottom: estimated error on [Fe/H] as a function of S/N for allmember stars. The total error is the quadrature sum of the random and systematicerror terms. Compare this figure to Figure 5.

the differences in [Fe/H] measured from the two different slit-masks. These measurements are different by up to 0.8 dex be-cause most of them (those observed on both slitmasks) are basedon partial exposures with low S/Ns. The bottom panel showsthe estimated uncertainty on metallicity versus S/N. These es-timates are based on the full exposures (co-added spectra fromboth slitmasks). Therefore, the bottom panel shows larger S/Nsthan the top panel. The trend of error with S/N is weaker than forradial velocities (Figure 5) because σMC for radial velocities wascalculated with Monte Carlo resampling of the observed spectra.Monte Carlo resampling was computationally prohibitive for es-timating uncertainties on [Fe/H]. As a result, we relied in parton σcovar instead of σMC,[Fe/H] for estimating the uncertainty on[Fe/H]. This quantity comes from the covariance matrix, whichtends to underestimate uncertainty compared to Monte Carlotechniques. Therefore, σsys,[Fe/H] accounts for the majority ofthe uncertainty in most stars, and the resulting error distributionshows only a weak trend with S/N.

In the following discussion, we have assumed that thesolar iron abundance is 12 + log n(Fe)/n(H) = 7.52 (Snedenet al. 1992). Also, we discarded metallicity measurements withuncertainties larger than 0.5 dex.

Another popular method of measuring metallicities of redgiants from low- to medium-resolution spectra is the empiricalrelation between [Fe/H] and the EW of the CaT. In order tocompare CaT metallicities to our synthetic spectral metallicities,we measured the EWs of the CaT lines at 8542 Å and 8662 Å.We fitted Lorentzian functions to each of the CaT lines. Weestimated uncertainties on EWs by Monte Carlo resampling. Weadded Gaussian random noise to each spectrum in proportionto its error spectrum. The amount of noise added to eachpixel was sampled from a Gaussian random distribution witha standard deviation equal to that pixel’s estimated Poissonnoise. We took the error on EW as the standard deviation of

−2

−1

0

[Fe/

H] C

aT

−2 −1 0[Fe/H]syn

−0.5

0.0

0.5

[Fe/

H] C

aT −

[Fe

/H] s

yn

Figure 11. Metallicities derived from the CaT vs. metallicities derived fromspectral synthesis.

100 such realizations. Then, we applied Starkenburg et al.’s(2010) calibration between CaT EW, absolute V magnitude,and [Fe/H]. This calibration was based on a combination ofGaussian fits and numerical integration in order to include thepressure-broadened wings of the CaT. As a rough substitute, weused the Lorentzian, which is a good approximation to both thecores and the wings of the CaT lines. We transformed extinction-corrected g0 and r0 magnitudes to Cousins V0 magnitudesusing Jordi et al.’s (2006) equations. We computed errorson [Fe/H]CaT by propagating the errors on EW and V. Wedid not include the uncertainty in the metallicity calibrationbecause it is significantly less than the substantial errors inEW. Figure 11 shows the comparison between [Fe/H] measuredfrom the CaT and from spectral synthesis for the stars where itwas possible to measure Lorentzian fits confidently. Althoughthe measurement uncertainties are large, the agreement isgood. This comparison reinforces credibility in our metallicitymeasurements based on Fe i lines. For the rest of this discussion,we used synthetic metallicities instead of the CaT metallicitiesbecause the synthetic metallicities are more precise for tworeasons. First, the synthetic metallicities do not require aconversion between photometric systems. Second, Fe i lines inthe DEIMOS spectrum of a typical moderately metal-poor redgiant have more signal (sum of EWs) than the combined CaT.

Figure 12 shows the metallicity distribution of member stars.The metallicities range from [Fe/H] = −2.3 to +0.0. The

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−2.5 −2.0 −1.5 −1.0 −0.5 0.0[Fe/H]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

df /

d[Fe

/H]

Pristine ModelPre−Enriched ModelExtra Gas Model

Pristine ModelPre−Enriched ModelExtra Gas Model

N = 61

Figure 12. Metallicity distribution for member stars. Error bars are calculatedwith Poisson statistics. Best-fitting, analytic models of chemical evolution areshown as colored curves. The red and blue lines overlap almost exactly.

(A color version of this figure is available in the online journal.)

shape of the distribution (a peak with a longer metal-poor tailthan a metal-rich one) is typical of dwarf galaxies of VV124’sstellar mass (Kirby et al. 2011a). The bottom of Table 3lists some additional shape characteristics of the metallicitydistribution.

We measured a mean metallicity of 〈[Fe/H]〉 = −1.14±0.06.This number is larger than previous photometric estimates:[Fe/H] = −1.37 (Kopylov et al. 2008; Tikhonov et al. 2010),[Fe/H] = −1.79 (Jacobs et al. 2011), [M/H] = −1.5 (in theoutskirts, B11a), and [M/H] = −1.4 (in the region 0.′5 <Rε < 1.′0, where Rε is the elliptical radius, Bellazzini et al.2011b). The metallicities measured by Jacobs et al. (2011) andBellazzini et al. (2011a, 2011b) are consistent because Jacobset al. measured [M/H] whereas Bellazzini et al. measured[Fe/H]. Jacobs et al. (2011) and Bellazzini et al. (2011a,2011b) also noted that the great majority of old RGB starshave [Fe/H] � −1.

Kirby et al. (2011a) fitted three analytic chemical evolutionmodels to the metallicity distributions of eight dSph satellitesof the Milky Way. The Simple Model is also known as a ClosedBox (Talbot & Arnett 1971). Its single parameter is the effectiveyield, p. Low effective yield indicates that the galaxy lost metals.Hence, we prefer the name “Simple Model” to “Closed Box.”The Pre-Enriched Model (Pagel 1997) is the Simple Model withthe additional parameter [Fe/H]0, which is the initial metallicityof the gas. The Extra Gas Model (Lynden-Bell 1975) allows forgas to fall into the galaxy during star formation. The infall rateis specifically chosen to allow for an analytic solution to themetallicity distribution. The parameter M quantifies the amountof infalling gas. The Extra Gas Model reduces to the SimpleModel in the limit M = 1.

We fitted the same models with the same maximum likelihoodestimation procedure as Kirby et al. (2011a). The coloredcurves in Figure 12 show the results. The curves for theSimple and Pre-Enriched Models nearly overlap because the

0.0 0.5 1.0 1.5 2.0 2.5 3.0elliptical distance (kpc)

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

[Fe/

H]

Figure 13. Metallicity as a function of elliptical distance from the center ofVV124. The elliptical distance is the semimajor axis of the ellipse (ε = 0.44)on which the star lies. The red line is a least-squares fit.

(A color version of this figure is available in the online journal.)

Pre-Enriched Model reduces to the Simple Model in the limitthat [Fe/H]0 = −∞. The maximum likelihood estimationcould not constrain a lower bound to [Fe/H]0. Hence, themetallicity distribution is consistent with initially metal-freegas. The metallicity distribution is more peaked than the SimpleModel. The Extra Gas Model roughly accounts for this peak. Infact, the Extra Gas Model is 5.9 times more likely to describethe metallicity distribution than the Simple Model. Metallicitydistributions consistent with gas inflow are typical for dSphswith the stellar mass of VV124 (Kirby et al. 2011a).

The low metallicity and highly sub-solar effective yields(p ≈ 0.1 Z�) require that VV124 lose some of its metals(see Kirby et al. 2011b), possibly in the form of supernovawinds. B11a also noted the role of gas flows into and out ofVV124. The H i gas distribution is asymmetric and suggestiveof gas flowing to or from the southeast of the galaxy’s star-forming center. The densest concentration of gas is also offsetto the southeast, further supporting the bulk motion of gas alongthat direction. While the present gas motions did not affect thepast star formation that made the bulk of the RGB, the radioobservations do support the role of gas flows in shaping thestellar population of VV124.

Radial metallicity gradients are typical of many galaxies, andmany dwarf galaxies are no exception (e.g., Tolstoy et al. 2004;Battaglia et al. 2006; Koch et al. 2006; Spolaor et al. 2009;Koleva et al. 2009a, 2009b; Kirby et al. 2011a). If gradients exist,they are always negative in the sense that metallicity decreaseswith increasing radius. Photometry strongly indicated that thestars near the center of VV124 are younger and more metal-rich (Tikhonov et al. 2010; Jacobs et al. 2011; Bellazzini et al.2011b). We confirmed a gradient of d[Fe/H]/dr = −0.26 ±0.04 dex kpc−1. Figure 13 shows the radial distribution of[Fe/H] along with an illustration of the gradient. Radial gra-dients can arise by several mechanisms. The most plausibleexplanation is that metallicity increased with time as super-novae enriched the interstellar medium with iron. Star for-mation also became more centrally concentrated because gasloss (due to supernova winds, for example) preferentially ex-pelled gas from the outer reaches of the galaxy. Therefore, theradial gradient arose because successive generations of starsbecame simultaneously more metal-rich and more centrallyconcentrated.

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The Astrophysical Journal, 751:46 (15pp), 2012 May 20 Kirby, Cohen, & Bellazzini

4

8

12

σ v (

km s

−1 )

6

7

8

log

M1/

2 (M

1

2

3

4

log

(M/L

V) 1

/2

1

2

3

log

(Mdy

n/M

*)1/

2

3 4 5 6 7 8-3

-2

-1

⟨[Fe

/H]⟩

3 4 5 6 7 8

Figure 14. Velocity dispersion, mass within the half-light radius, mass-to-light ratio within the half-light radius, dynamical-to-stellar mass ratio within the half-lightradius, and average metallicity vs. stellar mass (left) and luminosity (right) for dSph and dwarf elliptical galaxies in the Local Group. VV124 is represented by a redstar. Dynamical quantities (σv , M1/2, (M/LV )1/2, and (Mdyn/M∗)1/2) were taken from Wolf et al. (2010), and references therein for all galaxies except Bootes I. ForBootes I, we adopted σv from Koposov et al. (2011), and we adjusted its mass accordingly. The stellar masses were taken from Woo et al. (2008) for the larger dSphsand Martin et al. (2008, using the values derived with the Kroupa et al. 1993 initial mass function) for the ultra-faint dSphs. The metallicities came from Kirby et al.(2011a) except for Carina (Helmi et al. 2006) and Bootes I (Martin et al. 2007).

(A color version of this figure is available in the online journal.)

7. DISCUSSION AND CONCLUSIONS

Since its recent relocation to the edge of the Local Group, thedwarf galaxy VV124 has received considerable scrutiny. How-ever, measurements of its radial velocity have been inconsistent.The galaxy also seemed to possess a disk of stars. We observedVV124 with Keck/DEIMOS, and we determined that its radialvelocity agrees with H i measurements. The stellar velocities wemeasured show no evidence of a disk rotating any faster than8.6 km s−1, but larger samples will be necessary to place stricterlimits on rotation.

We gave an estimate of the dynamical mass of VV124 anddetermined that the mass of its stars alone does not account forthe velocity dispersion. Therefore, VV124 contains dark matter.Its mass-to-light ratio agrees with dSphs of similar stellar mass.

The metallicity distribution is also similar to dSphs of similarstellar mass. The average metallicity, metallicity dispersion, andshape of the distribution are nearly indistinguishable from dSphslike Leo I or Fornax. As is typical for large dSphs, the metallicitydistribution fits a chemical evolution model with infalling gasbetter than a Closed Box Model.

The parameters we derived from new spectroscopy suggestthat VV124 is a dIrr far along on its transformation into adSph. Figure 14 shows that VV124 lies along the same trendsdefined by other dSphs and dwarf elliptical galaxies in the LocalGroup. Thus, the galaxy is an excellent test case for models thatposit that dIrrs evolve into dSphs by the removal of gas andrandomization of stellar velocities. This process may happen inisolation or in the vicinity of a much larger galaxy, such as theMilky Way.

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The transformation of a dIrr into a dSph might proceedwithout the benefit of a dense environment. For example,VV124 in its present form could have resulted from a mergerof two dwarf galaxies ∼1 Gyr ago (D’Onghia et al. 2009;Kazantzidis et al. 2011b). The merger would have disrupteda disk and possibly triggered the starburst that Jacobs et al.(2011) observed. Recent simulations showed that ultravioletbackground radiation and stellar feedback are sufficient to expelall of the gas from a dwarf galaxy (Sawala et al. 2010). Thechallenge in these models is the formation of disk-less dSphs.It is possible that VV124 could have formed as a dispersion-supported galaxy, but this scenario runs contrary to the view thatdwarf galaxies formed as disks from which supernova feedbackremoved gas with low angular momentum (Governato et al.2010). Another challenge is to explain the low gas fraction ofVV124 relative to other isolated dwarf galaxies. In a sample of39 dwarf galaxies with stellar masses from Woo et al. (2008)and gas masses from Grebel et al. (2003), the only galaxies withlower gas fractions than VV124 (fgas = 0.09) are satellites ofthe Milky Way or M31, not isolated dwarfs like VV124.

The tidal stirring model (Mayer et al. 2001a, 2001b) explainsthe transformation from dIrrs to dSphs in the context of galaxyenvironment. This model posits that disky dIrrs lose their gasthrough ram pressure stripping in a group environment. Thestars then lose their rotational structure by tidal interactions.Numerous simulations address the transformation of dIrrs todSphs by tidal stirring (e.g., Klimentowski et al. 2009a; Łokaset al. 2010, 2011; Kazantzidis et al. 2011a). The stated goal ofmost of these simulations is to construct a spheroid from a disk.As a result, few studies address the kind of morphology peculiarto VV124 (a spheroid with a very faint disk-like feature).Nonetheless, the intermediate stages of some tidal stirringsimulations resemble a spheroid with a disk. The simulatedtidally stirred dwarf galaxy in Figure 12 of Mayer et al. (2001b)is a decent representation of VV124, but the “disk” is actuallytidal tails. Our radial velocity observations of stars in the wingsof VV124 do not support their interpretation as a disk. Hence,they may be tidal tails. However, tidal tails near apocenter areexpected to be elongated toward the perturber (Klimentowskiet al. 2009b). The disk- or tail-like feature observed in VV124must be nearly perpendicular to the Milky Way, and the greatcircle that connects VV124 and M31 intersects the major axis ofVV124 at an angle of 54◦. Therefore, the elongated photometricfeatures are unlikely to be tidal tails resulting from an interactionwith either of the large spiral galaxies of the Local Group.

Furthermore, VV124 is in a remote corner of the Local Group,highly isolated from other galaxies. Karachentsev et al. (2009)concluded that VV124 resides outside the zero-velocity surfaceof the Local Group. Because its velocity relative to the LocalGroup’s barycenter is positive, it will never enter the groupin the future. Additionally, B11a calculated that the intragroupmedium around VV124 is probably not dense enough to removegas by ram pressure stripping. As a result, tidal stirring wouldrequire that VV124 passed near another galaxy and subsequentlytraveled ∼1 Mpc to its current position. Traveling such a largedistance after a tidal interaction is not out of the question. Adwarf galaxy that passed within half of the virial radius ofa massive halo could have traveled up to several virial radiibeyond that massive halo (Lin et al. 2003; Ludlow et al. 2009;M. Teyssier et al. 2012, in preparation). As many as 10% of alldark matter halos are actually ejected subhalos that can be foundas far away as four virial radii from their former hosts (Wanget al. 2009). VV124 qualifies as a candidate subhalo ejected

from either the Milky Way or M31. Its low velocity relative tothe Local Group would require VV124 to be near its apocenter.Such a location would not be surprising given its large distancefrom the nearest massive halo. It also makes sense that we wouldobserve an ejected subhalo near its apocenter because subhaloslinger near their apocenters. As a potentially ejected satellitegalaxy, VV124 could be an example of tidal stirring. In thisscenario, a brief, high-speed passage near the Milky Way orM31 removed most of its gas, and the violent change in tidalforce near pericenter disrupted its stellar disk. A single passage issufficient for ram pressure stripping to remove most or all of thegas in a galaxy of VV124’s circular velocity (Mayer et al. 2006),but most simulations of tidal stirring require multiple pericentricpassages to transform a disk into a spheroid (Kazantzidis et al.2011a).

The tidal stirring explanation requires special circumstances.First, VV124 had to have been ejected from the Milky Way orM31, possibly in a multi-body encounter. Second, the stellardisk would have to be disrupted in just one pericentric passage,or VV124 would have had to acquire a large amount of orbitalenergy in a multi-body encounter on a subsequent pericentricpassage. Third, the tidal tails—if indeed the photometric wingsare tidal tails—would have to somehow point in a direction awayfrom the former host galaxy.

While our observations support the interpretation of VV124as a galaxy of a type between dIrr and dSph, they do notexplain how it came to be that way. We look forward to futuresimulations that will manufacture a digital replica of VV124:an isolated, mostly spheroidal dwarf galaxy that somehow lostmost of its gas but retained wispy, minimally rotating wings.

We are grateful to the many people who have worked to makethe Keck Telescope and its instruments a reality and to operateand maintain the Keck Observatory. The authors wish to extendspecial thanks to those of Hawaiian ancestry on whose sacredmountain we are privileged to be guests. Without their generoushospitality, none of the observations presented herein wouldhave been possible.

We thank Marla Geha for providing radial velocity templatespectra observed with DEIMOS and for her generous assistancein measuring radial velocities. We also thank the referee for adetailed report that greatly improved this manuscript. Supportfor this work was provided by NASA through Hubble Fellow-ship grant 51256.01 awarded to E.N.K. by the Space TelescopeScience Institute, which is operated by the Association of Uni-versities for Research in Astronomy, Inc., for NASA, undercontract NAS 5-26555. J.G.C. thanks NSF grant AST-0908139for partial support.

Facility: Keck:II (DEIMOS)

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